In order for anyone to really give a good answer to any of your questions, I think you need to be a little more specific.
If the tiles in the backsplash aren't flush, the only reasons would be inadequate substrate, or poor workmanship. If the substrate was inadequate, he should have informed you prior to starting, or should have prepared a more adequate base. Putting a tile backerboard in would require removing your counters (most likely), or cutting out drywall. If you had plaster, it is a totally different ballgame. I guess having tiles that aren't flush could mean a lot of things, how "not flush" are they? If they are really clearly not flush from a distance, sounds like a poor job, in any case. On the other hand, expecting tiles to be perfectly flush may be a poor expectation. I can't really give a good answer unless I know how far off they are; it could be that he just shuved the tiles in haphazardly, resulting in imperfections in the set depth.
With respect to the washboard appearance, it sounds like a problem with gluing the new counter laminate down. I wouldn't recommend doing what he did, or for that matter what you requested, and generally recommend purchasing new countertops with the laminates already applied. It almost sounds to me like he used OSB or failed to roll out the glue properly, which would be a serious error in either case. Purchasing finished countertop is a much better bet in the long run, here's why. Factory built countertops use much better processes than any carpenter can ever apply in the field. It doesn't help solve your problem, but it sounds like you tried an inexpensive solution and are now disappointed. It doens't provide cause for poor workmanship, but it might be difficult to get the contractor to oblige anything on the work. It really sounds like you went with the cheapest solution and got the cheapest workmanship, but I could be wrong.
I'd recommend contacting the contractor and discussing your concerns, he might be willing to make some corrections or refund some of the money, but the problem is, he doesn't sound like a great contractor in the first place, so you might be best off trying this one in court, and you certainly don't want any more of his work.